Mathematics textbooks teach logical reasoning by example, a practice started by Euclid; while logic textbooks treat logic as a subject in its own right without practical application to mathematics. Stuck in the middle are students seeking mathematical proficiency and educators seeking to provide it. To assist them, the article explains in practical detail how to teach logic-based skills such as: making mathematical reasoning fully explicit; moving from step to step in a mathematical proof in logically correct ways; and checking to (...) make sure inferences are logically correct. The methodology can easily be extended beyond the four examples analyzed. (shrink)

An epistemology of art has seemed problematic mainly because of arguments claiming that an essential element of a theory of knowledge, truth, has no place in aesthetic contexts. For, if it is objectively true that something is beautiful, it seems to follow that the predicate “is beautiful” expresses a property – a view asserted by Plato but denied by Hume and Kant. But then, if the belief that something is beautiful is not objectively true, we cannot be said to know (...) that something is beautiful and the path to an epistemology of art is effectively blocked. The article places the existence aesthetic properties in the proper context; presents a logically correct argument for the existence of such properties; identifies strategies for responding to this argument; explains why objections by Hume, Kant, and several other philosophers fail; and sketches a realization account of beauty influenced by Hogarth. (shrink)

Degas, Manet, Picasso, Dali and Lipchitz produced works of art exemplifying a seeming impossibility: Not only combining incompatible attributes but doing so consistently with aesthetic strictures Horace formulated in Ars Poetica. The article explains how these artists were able to do this, achieving what some critics have called ‘a new art,’ ‘a miracle,’ and ‘a new metaphor.’ The article also argues that the author achieved the same result in sculpture by means of philosophical analysis – probably a first in the (...) history of art. (shrink)

Definitions I presented in a previous article as part of a semantic approach in epistemology assumed that the concept of derivability from standard logic held across all mathematical and scientific disciplines. The present article argues that this assumption is not true for quantum mechanics (QM) by showing that concepts of validity applicable to proofs in mathematics and in classical mechanics are inapplicable to proofs in QM. Because semantic epistemology must include this important theory, revision is necessary. The one I propose (...) also extends semantic epistemology beyond the ‘hard’ sciences. The article ends by presenting and then refuting some responses QM theorists might make to my arguments. (shrink)

A theory purporting to solve the problem of universals must be able to explain predication, recurrence, and classification. How Platonism does this is well known. Here I take a hard look at an attempt by M.J. Cresswell to give an Aristotelian answer and show it to be a complete and utter failure. The answer does not eliminate commitment to universals and it is only half an answer anyway because it does not cover relational predicates, an omission that Russell noted dooms (...) answers by other philosophers as well. (shrink)

Philosophers have recognized for some time the usefulness of semantic conceptions of truth and belief. That the third member of the knowledge triad, evidence, might also have a useful semantic version seems to have been overlooked. This paper corrects that omission by defining a semantic conception of evidence for science and mathematics and then developing a semantic conception of knowledge for these fields, arguably mankind’s most important knowledge repository. The goal is to demonstrate the advantages of having an answer to (...) the more modest question “What is necessary and sufficient for introducing a knowledge predicate into scientific and mathematical languages?” – as contrasted with the ambitious Platonic question “What is knowledge?” After presenting the theory, the paper responds to a wide range of objections stemming from traditional philosophical concerns. (shrink)

Brought about through philosophical analysis – a first in the history of art – paradigm shifts in the ontology and epistemology of sculpture are described, motivated, and exemplified with pieces they inspired. Navigating the new aesthetic environment requires an ‘escape from Plato's Cave’ by means of a kind of phenomenological reduction. The new conceptual foundation allows artists unprecedented levels of freedom to explore and innovate, connects sculpture to music, and has the potential to enhance significantly the appreciation of art and (...) its impact on contemporary culture. The algorithmic nature of my paradigms shows that art and science have more in common than previously thought. (shrink)

Arnold Cusmariu ABSTRACT: Degas, Manet, Picasso, Dali and Lipchitz produced works of art exemplifying a seeming impossibility: Not only combining incompatible attributes but doing so consistently with aesthetic strictures Horace formulated in Ars Poetica. The article explains how these artists were able to do this, achieving what some critics have called ‘a new art,’ ‘a...

Following up on its predecessor in this Journal, the article defends philosophy as a guide to making and analyzing art; identifies Cubist solutions to the Prometheus Challenge, including a novel analysis of Picasso’s Les Demoiselles d’Avignon; defines a new concept of aesthetic attitude; proves the compatibility of Prometheus Challenge artworks with logic; and explains why Plato would have welcomed such artworks in his ideal state.

I present a formally explicit statement of Church's celebrated argument against Carnap's analysis of belief and defend it against well-known objections by W.V.O. Quine, R.M. Martin, and Michael Dummett.

Norman Malcolm has maintained that impure memory is a de dicto mixture of factual memory and later knowledge or inference. E. Stiffler objects that impure memory must be given a de re analysis because later knowledge must be applied to earlier memory to yield impure memory. I show that the conditions of Stiffler's de re analysis are neither necessary nor sufficient and that Malcolm can easily give a de dicto solution to the application problem.

Platonism considers existence as well as nonexistence as genuine properties. Kant and others have denied the former and the latter seems absurd. I reply that critics have forgotten that Platonism means accepting properties that are neither exemplified (like being a unicorn) nor exemplifiable (like nonexistence). I also present a Platonist analysis of negative existentials without appealing to nonexistence.

According to Platonism, "Socrates is wise" expresses the exemplification by Socrates of the property of being wise; while "Simmias is taller than Socrates" expresses the exemplification by <Simmias, Socrates> of the relation of being taller than. What about "Socrates is as tall as Socrates"? Is this property or relation exemplification? I show there is an answer that solves Russell's Paradox, Plato's "Third Man" argument, and the Greeling-Nelson paradox of non-self-applying terms.

Generations of scholars have worked to clarify the structure and content of the TMA, one of the most famous arguments in the history of philosophy. Though progress has been made, I show that a premise crucial to the argument has yet to be stated openly. This premise holds the way out of the predicament that enables Plato to retain intact the foundations of the Theory of Forms.

Cinema is an effective medium for communicating the Platonist attitude toward Beauty as an attribute worthy of moral respect, as case studies can illustrate. Mine focuses on the work of the French actress Carole Bouquet, who launched her career in Buñuel’s Cet obscur objet du désir (That Obscure Object of Desire). Part 1 shows sins against Beauty to be a unifying theme of Bouquet’s films, which leave no doubt as to the appropriate response. Part 2 combines Plato’s distinction in the (...) Phaedrus between erotic and aesthetic vision with insights from Kant and Baudelaire to sketch a course of action that addresses the critical “What is to be done?” question. (shrink)

An argument structure that covers both cases Gettier described in his 1963 paper reinforces the conclusion of my 2012 Logos & Episteme article that the justified true belief (JTB) conception of knowledge is inconsistent. The stronger argument makes possible identification of fundamental flaws in the standard approach of adding a fourth condition to JTB, so that a new kind of skepticism becomes inevitable unless conceptual change occurs.

W.V.O. Quine has famously objected that (1) properties are philosophically suspect because (2) there is no entity without identity and (3) the synonymy criterion for property identity won't do because there's no such concept as synonymy. (2) and (3) may or may not be right but do not prove (1). I reply that Leiniz's Law handles property identity, as it does for everything else, then respond to a variety of objections and confusions.

Arnold Cusmariu ABSTRACT: The Cogito formulation in Discourse on Method attributes properties to one conceptual category that belong to another. Correcting the error ends up defeating Descartes’ response to skepticism. His own creation, the Evil Genius, is to blame. Download PDF.

Arnold Cusmariu ABSTRACT: Following up on its predecessor in this Journal, the article defends philosophy as a guide to making and analyzing art; identifies Cubist solutions to the Prometheus Challenge, including a novel analysis of Picasso’s Les Demoiselles d’Avignon; defines a new concept of aesthetic attitude; proves the compatibility of Prometheus Challenge artworks with logic;...

Am şlefuit materia pentru a afla linia continuă.Und das Problem ensteht: was is das, was übrigbleibt, wenn ich von der Tatsache, daß ich meinen Arm hebe, die abziehe, daß mein Arm sich hebt?Acknowledged to have launched modern poetry with Les Fleurs du mal, Charles Baudelaire was also a prolific and influential art critic, a close friend of Edouard Manet, and an early champion of Eugène Delacroix. At one time decidedly not a friend of sculpture, Baudelaire published a critique of this (...) art form in a section of his Salon de 1846 titled “Pourquoi la sculpture est ennuyeuse” :3Sculpture has several disadvantages inherent in the medium itself. Crude and direct like nature, sculpture is.. (shrink)

Gilbert Ryle has argued that Plato's Theory of Forms is a "logically vicious" doctrine because it's fundamental concept of exemplification leads to a vicious infinite regress. David Armstrong and Alan Donagan have agreed with Ryle. After making Ryle's argument logically explicit, I show the exemplification regress is illusory. Exemplification is a genuine universal alongside other relations; there is nothing paradoxical in its being exemplified over and over and over ... Platonism can define logical properties of this relation but not the (...) relation itself, however. (shrink)

I attempt to rescue Frege's naive conception of a set according to which there is a set for every property by redefining the technical concept of degree of an open sentence. Instead of making degree a function of the number of free variables, I make it a function of free variable occurrences. What Russell proved, then, is that there is not a relation-in-extension for every relation-in-intension. In a brief paper it is not possible to discuss how redefining the function-argument correlation (...) affects Frege's system. (shrink)

In "Translation and Belief" I presented a two-stage version of Church's translation argument against Carnap's analysis of belief. Here I show that the first stage is sufficient to establish a weaker, though no less significant conclusion, if supplemented with the principle that the same thought or idea can be expressed in different languages.

A valid and arguably sound private language argument is built using premises based on Wittgenstein’s Philosophical Investigations augmented by familiar analytic distinctions and concepts of logic. The private language problem and the solution presented here can be plausibly traced to Plato’s Allegory of the Cave. Both literatures missed the connection.

The article demonstrates unity in Plato’s thought to a degree not heretofore realized and suggests analytical links to developments in logic, metaphysics and epistemology millennia later, substantiating Whitehead's famous comment that ‘the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.’.

I give the following analysis of de re belief: S believes with respect to X that it has the property F =df S believes a proposition which is for S extensionally to the effect that it has the property F. I spell this definition out and defend it against objections by M. Pastin, commenting also on his account of de re belief.

Logical reasoning is explained in ways young children can understand and apply. Concepts of a difficult and complex subject are made interesting, fun and easy to grasp thanks to a playful and friendly approach free of jargon. -/- .

Tackling the question whether beauty is a property as if the problem of universals could safely be ignored leads to confusions exemplified in Scruton 2009, McMahon 2007, Zangwill 2001 and Scarry 1999, among recent writers. I frame the question in the proper context with a measure of precision, clear away misunderstandings, present a logically valid argument for an affirmative answer, list three relevant and four irrelevant ways of countering the argument, and show that well-known views of Hume and Kant yield (...) relevant objections only if construed in Russellian terms, but still fail. Finally, I sketch a realization account of beauty along Platonist lines, similar to Hogarth’s. (shrink)

Considerable effort has gone into clarifying the structure and the content of the Third Man Argument. Nevertheless, the argument is still an enthymeme. A premise crucial to it has yet to be stated openly. This premise holds the way out of the predicament which, happily, enables Plato to retain intact the foundations of the Theory of Forms. The solution proposed allows us in addition to look beyond the TMA and place this ancient argument in the context of an important modern (...) insight. (shrink)

In "The Problems of Philosophy," Russell held that universals not exist, rather, they subsist. In the same work, he stated that universals are nevertheless "something," without intending to suggest that quantification over universals would require a special quantifier. I show these apparently conflicting statements can be reconciled with a simple definition of "subsists.".

Exemplifying with sculptures the author created, the article shows that ontological algorithms can yield aesthetic content, while epistemological algorithms can capture it. Bridging the gap between art and logic creates new and exciting aesthetic opportunities, allaying Henry Moore’s fears of ‘paralysis by analysis.’ On the flip side, appreciating all that algorithmic art has to offer poses intellectual challenges that run counter to subjectivist approaches to art and its education.

The Cogito formulation in Discourse on Method attributes properties to one conceptual category that belong to another. Correcting the error ends up defeating Descartes’ response to skepticism. His own creation, the Evil Genius, is to blame.

"Arguing that debates over legitimacy, political violence, freedom, and justice would benefit greatly from cross-tradition theorizing, this book shows how putting analytic and continental political theory in conversation would help us to overcome these intractable problems"--.

A most sensible exposition of Nietzsche's philosophy.

Am 6. Dezember 1915 und am 8. Januar 1916 legte Arnold Sommerfeld der Bayerischen Akademie der Wissenschaften zwei Abhandlungen im Umfang von 75 Druckseiten vor, mit denen er das Bohrsche Atommodell aus dem Jahr 1913 zur Bohr-Sommerfeldschen Atomtheorie erweiterte. In Sommerfelds Gesammelten Schriften findet sich nur die im Juli 1916 von Sommerfeld in den Annalen der Physik eingereichte Publikation darüber. "Meine Spektrallinien sind endlich in der Akademie in’s Unreine gedruckt. In den Annalen werden sie in geläuterter Form erscheinen", so (...) hatte Sommerfeld am 10. Februar 1916 dem Herausgeber der Annalen der Physik diese Publikation angekündigt. Aus wissenschaftshistorischer Sicht sind für die Erweiterung der Bohrschen Atomtheorie jedoch gerade die vor dem Läuterungsprozess publizierten Akademieabhandlungen von besonderem Interesse. Der Reproduktion dieser Akademieabhandlungen wird ein ausführlicher physikhistorischer Essay (ca. 100 Druckseiten) vorangestellt. (shrink)

"As a 'rhetoric of the mean' (mesotes ideal), sensibility provides a positive catalog of emotionalization. This is because ethos as an emotional level is viewed as being able, through gentle emotions, to please, placate and achieve sympathy and virtue (Quintilian). Sensibility in literature creates a bridge between an 'art of the soul' that developed into a major subjective and personal factor in the 18th century and a sense of sociability that aimed to integrate the individual into the community. The goal (...) of this study is to provide, through a structural linking of the ethos of virtue and the 'rhetoric of the mean', a reading of literature of sensibility based on rhetoric and cultural history that can explain both its public success 'with the people' and the reasons for why it failed to meet its own claims."--Publisher's website. (shrink)

This book explores the relationship between scientific fact and metaphysical reality, offering a fresh perspective on the intersection of these two seemingly disparate fields. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual (...) or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

First published in 1959, this book is concerned with the methodology of art history, and so with questions about historical thinking; it enquires what scientific history of art can accomplish, what are its mean and limitations? It contains philosophical reflections on history and begins with chapters on the scope and limitations of a sociology of art, and the concept of ideology in the history of art. The chapter on the concept of "art history without names" occupies the central position in (...) the book -- thoroughly discussing the basic philosophical outlook for the whole work. There are also further chapters on psychoanalysis, folk art and popular art. The chapter on the role of convention in the history of art points the way for further study. (shrink)

Ce papier présente le corpus des discours du Premier ministre anglais (Tony Blair) prononcés de 1997 à 2004. Avant d'être intégrés dans le corpus, les textes sont corrigés, les graphies sont standardisées. On montre que ce corpus ouvre de nombreuses pistes de recherches. Deux exemples sont donnés : les principales ruptures thématiques et stylistiques permettent de repérer deux grandes périodes dans ces huit années ; on caractérise la richesse du vocabulaire de T. Blair à l'aide des notions de spécialisation et (...) de diversité. (shrink)